5. The random variable \(X\) has a continuous uniform distribution on the interval \(a \leq X \leq 3 a\).
- Without assuming any standard results, prove that \(\mu\), the mean value of \(X\), is equal to \(2 a\) and derive an expression for \(\sigma ^ { 2 }\), the variance of \(X\), in terms of \(a\).
- Find the probability that \(| X - \mu | < \sigma\) and compare this with the same probability when \(x\) is modelled by a Normal distribution with the same mean and variance.
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